Tricritical points in the Sherrington-Kirkpatrick model in the presence of discrete random fields

摘要

The infinite-range-interaction Ising spin glass is considered in the presence of an external random magnetic field following a trimodal (three-peak) distribution. Such a distribution corresponds to a bimodal added to a probability po for a field dilution, in such a way that at each site the field h(i) obeys P(h(i))=p+delta(h(i)-h(0)) +p(0)delta(h(i))+p(-)delta(h(i)+h(0)). The model is studied through the replica method and phase diagrams are obtained within the replica-symmetry approximation. It is shown that the border of the ferromagnetic phase may present, for conveniently chosen values of p(0) and h(0), first-order phase transitions, as well as tricritical points at finite temperatures. Analogous to what happens for the Ising ferromagnet under a trimodal random field, it is verified that the first-order phase transitions are directly related to the dilution in the fields: the extensions of these transitions are reduced for increasing values of p(0). Whenever the delta function at the origin becomes comparable to those at h(i)=+/-h(0), first-order phase transitions disappear; in fact, the threshold value p(0)*, above which all phase transitions are continuous, is calculated analytically as p(0)*=2(e(3/2)+2)(-1)approximate to 0.30856. The ferromagnetic boundary at zero temperature also exhibits an interesting behavior: for 0(0)(0)*, a single tricritical point occurs, whereas if p(0)>p(0)* the critical frontier is completely continuous; however, far p(0)=p(0)*, a fourth-order critical point appears. Stability analysis of the replica-symmetric solution is performed and the regions of validity of such a solution are identified; in particular, the Almeida-Thouless line in the plane field versus temperature is shown to depend on the weight p(0). [References: 64]